the number of wins in a season for 32 randomly selectedprofessional football tea

Question

the number of wins in a season for 32 randomly selectedprofessional football teams are listed below. Construct a 90%confidence interval for the true mean number of wins in aseason 9    9   9    8    10   9  7     2 11 10   6    4    11    9  8     8 12 10   7    5    12    6   4    3 12   9   9     7    10   7   7     5
   the number of wins in a season for 32 randomly selectedprofessional football teams are listed below. Construct a 90%confidence interval for the true mean number of wins in aseason 9    9   9    8    10   9  7     2 11 10   6    4    11    9  8     8 12 10   7    5    12    6   4    3 12   9   9     7    10   7   7     5
  

Explanation / Answer

sample size, n = 32 sample mean, x=7.97 standard deviation, s = 2.62 standard error, e = s/n = 2.62/32 =0.46 for 90% confidence, z = 1.65     (from ztable) hence , confidence interval, CI = x ± ze = 7.97 ± (1.65*0.46) = (7.211, 8.729)

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